Antisense technology (treatment directed against blocking "sense" mRNA) represents a novel approach to the treatment of cancer and other proliferative diseases. The H-ras oncogene and its protein product are known to play an important role in the development and progression of many cancers. The study will determine the maximum tolerated dose of ISIS 2503 in patients with advanced cancer when administered as a weekly 24-hour continuous i.v. infusion. The secondary objectives of this study are to characterize the safety profile and pharmacokinetic and pharmacodynamic of ISIS 2503 when administered as a weekly 24-hour continuous i.v. infusion.